&Bullet; physics 14, p76

Several sources of mechanical dissipation appear to explain why a cantilever exposed to an extreme temperature gradient has less thermal noise than theory predicts.

L. Bellon / ENS de Lyon

The assumption that a system is in thermal equilibrium is a common physical approximation. But in the real world this condition is seldom met. Now, Alex Fontana of the École Normale Supérieure in Lyon, France, and colleagues have updated the fluctuation-dissipation theorem (FDT) – a tool used to estimate the thermal noise of a physical system – to reflect the thermal noise of an unbalanced micro-cantilever [1] .

In previous experiments, researchers had seen that a silicon micro-cantilever, significantly hotter at one end than the other, vibrated as if it were a room temperature object in thermal equilibrium. The temperature gradient in these experiments was several hundred degrees over several hundred micrometers. By applying FDT to this out of balance system, the researchers predict mechanical fluctuations much higher than those found in the experiments. In new experiments, Fontana and colleagues have taken an arm to another extreme. They cryogenically cooled the base of a millimeter-long cantilever and heated its tip to the melting point, giving the cantilever ends a temperature difference of around 1700 K. In this experiment, the researchers showed a lack of variability that was similar to the previous work.

Fontana and colleagues propose a theoretical framework to explain the phenomenon that includes an update of the FDT. They show that they can fix the discrepancy between theory and experiment by including mechanical dissipation with two components. The first component is a “pinch loss” – a loss of mechanical energy through the base of the boom. The second is “distributed damping,” which means that mechanical fluctuations are lost over the entire length of the boom.

The researchers say their results could help improve precision measurements that are affected by mechanical fluctuations, such as the interferometers used in gravitational wave detectors.


  1. A. Fontana et al., “Thermal noise of a cryo-cooled silicon cantilever that is locally heated up to its melting point”, Phys. Rev. E103, 062125 (2021).

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